Sally Jameson Valuing Stock Option in a Compensation Package-Result.pdf

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1、FinancialEngineeringCaseStudySallyJameson:ValuingStockOptioninaCompensationPackage2012/5/31CASEREVIEWMs.JamesonwasfacingachoicewhenshegotherfirstjobafterthegraduationofherMBAdegree.WhenshefoundawonderfuljobinthecompanyTelstar,shecangetbonusbesidestheregularsalary.Nowshehadthechoiceo

2、feither$5,000incashor3,000optionsonTelstar’sstocks.Thedetailedinformationcanbeasfollows:EachoptiongrantedtheownertobuyoneshareofTelstarstockat$35ontheexact5yearslater.Thespotpriceofthatstockis$18.75.ButtheoptionwillberejectedifSallyleavesthecompanyduringthefirstfiveyears.Nowtheprobl

3、emSallyfacedwithiswhethersheshouldgetbonusincaseorbonusasoptions.Alsosomemarketdataaregiveninthecase.QUESTIONANSWERQUESTION1WhatistheimpliedvolatilityoftheTelstarcallwithastrikepriceof$20andanexpirationdateofJanuary22,1994?ANSWERUsingExcel,weformtheBlack‐ScholesFormula,sothatwecanus

4、ethefunctionofsinglevariablesolutiontogettheimpliedvolatility.Wehavealreadyknownstockprice,exercisepriceandoptionprice.FromMay27,1992toJan22,1994,thereare604daysleft,soit’snearly1.65years.Inaddition,wehavegotthetableofTreasuryBonds’BEY(BondEquivalentYield),soallweneedtodoistochanget

5、hemintocontinuouscompoundedrates.1000െP1∵BEYൌൈPT1000∴ሺ1൅rሻ୘ൌൌBEYൈT൅1P౐∴rൌ √BEYൈT൅1െ1Andcc=ln(1+r)BEYrcc1year4.02%4.02%3.94%2year5.25%5.12%4.99%1.65year4.74%4.63%Thenwecaninputthesevariablestothespreadsheet,andgettheimpliedvolatilityofthiscalloptiontobe38.4%Currentpriceofunderlyingco

6、mmonS=18.75stockExercisepriceK=20Risk-freerate(continuouslyr=4.63%compounded)Timetoexpirationt=1.65Volatility(continuouslycompounded)σ=38.40%Callvalue3.75QUESTION2IfweignoretaxconsiderationsandassumethatSallyJamesonisfreetosellheroptionsatanytimeaftershejoinsTelstar,whichcompensatio

7、npackageisworthmore?ANSWERFirstofall,weshouldfindoutthecharacteristicsforthestockoptionsinthatcompensationpackage.Fromthesentence“theoptionsrepresenttherighttobuyTelstarstockatasetprice,afterasetperiodoftime”,wecanknowthattheoptionsareEuropeanOptions.Itsstrikepriceis$35,itsmaturityi

8、s5years.Thecurrents